Learning Stable Deep Dynamics Models

TL;DR

This paper introduces a method for learning deep dynamical models with guaranteed stability across the entire state space by jointly learning a dynamics model and a Lyapunov function, enabling modeling of complex systems.

Contribution

It proposes a novel approach that ensures stability in deep dynamical models through joint learning of dynamics and Lyapunov functions, extending to complex dynamics like video textures.

Findings

Successfully models simple dynamical systems with stability guarantees.

Can be combined with deep generative models for complex dynamics.

Demonstrates end-to-end learning of stable, complex dynamical behaviors.

Abstract

Deep networks are commonly used to model dynamical systems, predicting how the state of a system will evolve over time (either autonomously or in response to control inputs). Despite the predictive power of these systems, it has been difficult to make formal claims about the basic properties of the learned systems. In this paper, we propose an approach for learning dynamical systems that are guaranteed to be stable over the entire state space. The approach works by jointly learning a dynamics model and Lyapunov function that guarantees non-expansiveness of the dynamics under the learned Lyapunov function. We show that such learning systems are able to model simple dynamical systems and can be combined with additional deep generative models to learn complex dynamics, such as video textures, in a fully end-to-end fashion.